How to check the RSA p,q,N,phi_N,e,d

As we know the RSA certificates

1. we will choose two primes p,q
2. N=p*q
3. phi_N = (p-1)*(q-1)
4. Then choose e, e.g. 65537
5. Then calculate the d, e*d % phi_N = 1
6. Then we have the public key (e, N), private key (d, N)

Now we got the certificates from let’s encrypt, so how can be get those values

1. cert1.pem
2. chain1.pem
3. fullchain1.pem
4. privkey1.pem

Here is one Python script that print all those details.

from cryptography import x509
from cryptography.hazmat.backends import default_backend
from cryptography.hazmat.primitives import serialization

def load_certificate(file_path):
    with open(file_path, 'rb') as f:
        cert_data = f.read()
    return x509.load_pem_x509_certificate(cert_data, default_backend())

def load_private_key(file_path):
    with open(file_path, 'rb') as f:
        key_data = f.read()
    return serialization.load_pem_private_key(key_data, password=None, backend=default_backend())

def display_certificate_details(cert):
    print("Issuer:", cert.issuer)
    print("Subject:", cert.subject)
    print("Serial Number:", cert.serial_number)
    print("Not Before:", cert.not_valid_before)
    print("Not After:", cert.not_valid_after)
    print("Public Key:", cert.public_key())

def display_private_key_details(key):
    print("Private Key Type:", type(key))
    print("Private Key:", key)

# Load and display details for each file
cert1 = load_certificate('cert1.pem')
chain1 = load_certificate('chain1.pem')
fullchain1 = load_certificate('fullchain1.pem')
privkey1 = load_private_key('privkey1.pem')

print("Certificate 1 Details:")
display_certificate_details(cert1)

print("\nChain 1 Details:")
display_certificate_details(chain1)

print("\nFull Chain 1 Details:")
display_certificate_details(fullchain1)

print("\nPrivate Key 1 Details:")
display_private_key_details(privkey1)


from cryptography.hazmat.primitives import serialization
from cryptography.hazmat.backends import default_backend

def load_private_key(file_path):
    with open(file_path, 'rb') as f:
        key_data = f.read()
    return serialization.load_pem_private_key(key_data, password=None, backend=default_backend())

def display_rsa_parameters(key):
    if key.private_numbers():
        private_numbers = key.private_numbers()
        public_numbers = private_numbers.public_numbers

        p = private_numbers.p
        q = private_numbers.q
        d = private_numbers.d
        e = public_numbers.e
        N = public_numbers.n
        phi_N = (p - 1) * (q - 1)

        print("p:", p)
        print("q:", q)
        print("e:", e)
        print("d:", d)
        print("N:", N)
        print("phi_N:", phi_N)
    else:
        print("The key is not an RSA private key.")

# Load the private key
privkey1 = load_private_key('privkey1.pem')

# Display RSA parameters
display_rsa_parameters(privkey1)

And here is the output

Certificate 1 Details:
Issuer: <Name(C=US,O=Let's Encrypt,CN=R3)>
Subject: <Name(CN=*.pjq.me)>
Serial Number: 399357001611271868934008942535231577601291
/Users/i329817/SAPDevelop/workspace/SECulum-Crypto-Examples/Other/CA.py:19: CryptographyDeprecationWarning: Properties that return a naïve datetime object have been deprecated. Please switch to not_valid_before_utc.
  print("Not Before:", cert.not_valid_before)
Not Before: 2024-03-11 03:37:02
/Users/i329817/SAPDevelop/workspace/SECulum-Crypto-Examples/Other/CA.py:20: CryptographyDeprecationWarning: Properties that return a naïve datetime object have been deprecated. Please switch to not_valid_after_utc.
  print("Not After:", cert.not_valid_after)
Not After: 2024-06-09 03:37:01
Public Key: <cryptography.hazmat.bindings._rust.openssl.rsa.RSAPublicKey object at 0x101310310>

Chain 1 Details:
Issuer: <Name(C=US,O=Internet Security Research Group,CN=ISRG Root X1)>
Subject: <Name(C=US,O=Let's Encrypt,CN=R3)>
Serial Number: 192961496339968674994309121183282847578
Not Before: 2020-09-04 00:00:00
Not After: 2025-09-15 16:00:00
Public Key: <cryptography.hazmat.bindings._rust.openssl.rsa.RSAPublicKey object at 0x101310310>

Full Chain 1 Details:
Issuer: <Name(C=US,O=Let's Encrypt,CN=R3)>
Subject: <Name(CN=*.pjq.me)>
Serial Number: 399357001611271868934008942535231577601291
Not Before: 2024-03-11 03:37:02
Not After: 2024-06-09 03:37:01
Public Key: <cryptography.hazmat.bindings._rust.openssl.rsa.RSAPublicKey object at 0x1013102f0>

Private Key 1 Details:
Private Key Type: <class 'cryptography.hazmat.bindings._rust.openssl.rsa.RSAPrivateKey'>
Private Key: <cryptography.hazmat.bindings._rust.openssl.rsa.RSAPrivateKey object at 0x1013101f0>
p: 132069789892654411168004522386293936563648260984708049888769058861400033840104922637240827355145535778467721990046061228393420363010924409941513508800258809981119101399937003195217979917259199066675447728576676098948661691324234988484581514373041670098119069924124636404134462689209640493314790132976282083611
q: 137105056982080406391028823084893501194543535606308088202698272087931645688882684542797221955650442538986772234601648478841035329665841202081550877179575957078786677686845060335508172755008305533505548942627696405948787947081088462002379085459968945063951380151782547161878405562777603813013479678683689059989
e: 65537
d: 756214848412734766389636904239299485009061447036919688389891952047609574545734290864923373793452280368637781527992131423339716753716888185459331923714856645280928404198259347205993579213846803666627529909232828722879650374490951581311985882248017934718743944682742282487622451272419143686155769738092352440521581984122740725976684511860250924537999931049740452351974285438729683375867711220177807812280621918795246117514339543091408571088210170010573980132856774272424920513332731618240977627013497573799860486533079269798618961305686700083116612832032852006212842303481886949894366447734991011109426370041918678153
N: 18107436068843769961592120494384716970785115109411255249546345948609495318598388096607410722799226196024630722689083053376476074858729887106484558379430237472333286381418093839181293825698895861125235085005989001100242472266354948404984880805585806133599679175254980258454991811852588023295429551087087505259481055918651153874312403039948814343657680828818579172724766105080872512340183146177770234401565111928007670988819164086328954605138596051183819569014922240750776080760982732900349444868680946505230852975887754348080529969823222341004758720100799077687160346328480228883962117022614977552611965834106892740279
phi_N: 18107436068843769961592120494384716970785115109411255249546345948609495318598388096607410722799226196024630722689083053376476074858729887106484558379430237472333286381418093839181293825698895861125235085005989001100242472266354948404984880805585806133599679175254980258454991811852588023295429551087087505259211881071776419056753369694477626905899489032227563034633298774131540832811195538997732185090769133610553176764171454379094498912461830439160755183035087473690870301674200669369623292196413441905049856304683381843183080331417898890517798120267788462525089896252573045317949248770627733246283696022446921596680

I wonder if one day I will be able to see the N here being factored into p*q by a quantum computer. If it can be factored, then phi_N can be obtained, and the private key (d, N) can be derived through 65537*d % phi_N = 1. Then the RSA certificate would be doomed.